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  1. Carl Craver (2007). Constitutive Explanatory Relevance. Journal of Philosophical Research 32:3-20.
    In what sense are the activities and properties of components in a mechanism explanatorily relevant to the behavior of a mechanism as a whole? I articulate this problem, the problem of constitutive relevance, and I show that it must be solved if we are to understand mechanisms and mechanistic explanation. I argue against some putative solutions to the problem of constitutive relevance, and I sketch a positive account according to which relevance is analyzed in terms ofrelationships of mutual manipulability between (...)
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  2. Michael E. Cuffaro (forthcoming). How-Possibly Explanations in Quantum Computer Science. Philosophy of Science.
    A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds, and in so doing to describe the possibility spaces associated with these processes. By doing this we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in (...)
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  3. James H. Fetzer (1972). Statistical Explanations. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1972:337 - 347.
    The purpose of this paper is to provide a systematic appraisal of the covering law and statistical relevance theories of statistical explanation advanced by Carl G. Hempel and by Wesley C. Salmon, respectively. The analysis is intended to show that the difference between these accounts is inprinciple analogous to the distinction between truth and confirmation, where Hempel's analysis applies to what is taken to be the case and Salmon's analysis applies to what is the case. Specifically, it is argued (a) (...)
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  4. Phyllis McKay Illari & Jon Williamson (2011). Mechanisms Are Real and Local. In Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.), Causality in the Sciences. Oup Oxford.
    Mechanisms have become much-discussed, yet there is still no consensus on how to characterise them. In this paper, we start with something everyone is agreed on – that mechanisms explain – and investigate what constraints this imposes on our metaphysics of mechanisms. We examine two widely shared premises about how to understand mechanistic explanation: (1) that mechanistic explanation offers a welcome alternative to traditional laws-based explanation and (2) that there are two senses of mechanistic explanation that we call ‘epistemic explanation’ (...)
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  5. Ernest Nagel (1951). Mechanistic Explanation and Organismic Biology. Philosophy and Phenomenological Research 11 (3):327-338.
  6. Ulrich Röseberg (1988). Historical Explanations in Modern Physics? The Lesson of Quantum Mechanics. International Studies in the Philosophy of Science 3 (1):68-79.
  7. C. Salmon Wesley (1970). Statistical Explanation. In Robert Colodny (ed.), The Nature and Function of Scientific Theories. University of Pittsburgh Press.
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  8. Wesley C. Salmon (1970). Statistical Explanation. In Robert Colodny (ed.), The Nature and Function of Scientific Theories. University of Pittsburgh Press. 173--231.
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  9. Douglas W. Shrader Jr (1977). Causation, Explanation, and Statistical Relevance. Philosophy of Science 44 (1):136-145.
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  10. J./P. Thomas (1979). Homogeneity Conditions on the Statistical Relevance Model of Explanation. Philosophical Studies 36 (1):101 - 105.
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  11. Jeroen Van Bouwel (2004). Questioning Structurism as a New Standard for Social Scientific Explanations. Graduate Journal of Social Science 1 (2):204-226.
    As the literature on Critical Realism in the social sciences is growing, it is about time to analyse whether a new, acceptable standard for social scientific explanations is being introduced. In order to do so, I will discuss the work of Christopher Lloyd, who analysed contributions of social scientists that rely on (what he called) a structurist ontology and a structurist methodology, and advocated a third option in the methodological debate between individualism and holism. I will suggest modifications to three (...)
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Functional Explanation
  1. Jonathan Birch (2012). Robust Processes and Teleological Language. European Journal for Philosophy of Science 3 (3):299-312.
    I consider some hitherto unexplored examples of teleological language in the sciences. In explicating these examples, I aim to show (a) that such language is not the sole preserve of the biological sciences, and (b) that not all such talk is reducible to the ascription of functions. In chemistry and biochemistry, scientists explaining molecular rearrangements and protein folding talk informally of molecules rearranging “in order to” maximize stability. Evolutionary biologists, meanwhile, often speak of traits evolving “in order to” optimize some (...)
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  2. Darren Bradley (2013). Functionalism and The Independence Problems. Noûs 47 (1):545-557.
    The independence problems for functionalism stem from the worry that if functional properties are defined in terms of their causes and effects then such functional properties seem to be too intimately connected to these purported causes and effects. I distinguish three different ways the independence problems can be filled out – in terms of necessary connections, analytic connections and vacuous explanations. I argue that none of these present serious problems. Instead, they bring out some important and over-looked features of functionalism.
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  3. Justin Garson (2011). Selected Effects and Causal Role Functions in the Brain: The Case for an Etiological Approach to Neuroscience. Biology and Philosophy 26 (4):547-565.
    Despite the voluminous literature on biological functions produced over the last 40 years, few philosophers have studied the concept of function as it is used in neuroscience. Recently, Craver (forthcoming; also see Craver 2001) defended the causal role theory against the selected effects theory as the most appropriate theory of function for neuroscience. The following argues that though neuroscientists do study causal role functions, the scope of that theory is not as universal as claimed. Despite the strong prima facie superiority (...)
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  4. Peter J. Graham (forthcoming). The Function of Perception. In Abrol Fairweather (ed.), Virtue Scientia: Virtue Epistemology and Philosophy of Science. Synthese Library.
    What is the biological function of perception? I hold perception, especially visual perception in humans, has the biological function of accurately representing the environment. Tyler Burge argues this cannot be so in Origins of Objectivity (Oxford, 2010), for accuracy is a semantical relationship and not, as such, a practical matter. Burge also provides a supporting example. I rebut the argument and the example. Accuracy is sometimes also a practical matter if accuracy partly explains how perception contributes to survival and reproduction.
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  5. Rolf Gruner (1966). Teleological and Functional Explanations. Mind 75 (300):516-526.
  6. Carl Hempel (1965). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. The Free Press.
  7. C. S. Jenkins & Daniel Nolan (2008). Backwards Explanation. Philosophical Studies 140 (1):103 - 115.
    We discuss explanation of an earlier event by a later event, and argue that prima facie cases of backwards event explanation are ubiquitous. Some examples: (1) I am tidying my flat because my brother is coming to visit tomorrow. (2) The scarlet pimpernels are closing because it is about to rain. (3) The volcano is smoking because it is going to erupt soon. We then look at various ways people might attempt to explain away these prima facie cases by arguing (...)
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  8. Ehud Lamm (2013). Theoreticians as Professional Outsiders: The Modeling Strategies of John von Neumann and Norbert Wiener. In Oren Harman & Michael Dietrich (eds.), Outsider Scientists: Routes to Innovation in Biology. Chicago University Press.
    Both von Neumann and Wiener were outsiders to biology. Both were inspired by biology and both proposed models and generalizations that proved inspirational for biologists. Around the same time in the 1940s von Neumann developed the notion of self reproducing automata and Wiener suggested an explication of teleology using the notion of negative feedback. These efforts were similar in spirit. Both von Neumann and Wiener used mathematical ideas to attack foundational issues in biology, and the concepts they articulated had lasting (...)
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  9. Martin Mahner & Mario Bunge (2001). Function and Functionalism: A Synthetic Perspective. Philosophy of Science 68 (1):75-94.
    In this paper we examine the following problems: How many concepts of function are there in biology, social science, and technology? Are they logically related and if so, how? Which of these function concepts effect a functional explanation as opposed to a mere functional account? What are the consequences of a pluralist view of functions for functionalism? We submit that there are five concepts of function in biology, which are logically related in a particular way, and six function concepts in (...)
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  10. Bence Nanay (2012). Function Attribution Depends on the Explanatory Context: A Reply to Neander and Rosenberg's Reply to Nanay. Journal of Philosophy 109 (10):623-627.
    In ‘A modal theory of function’, I gave an argument against all existing theories of function and outlined a new theory. Karen Neander and Alex Rosenberg argue against both my negative and my positive claim. My aim here is not merely to defend my account from their objections, but to (a) very briefly point out that the new account of etiological function they propose in response to my criticism cannot avoid the circularity worry either and, more importantly, to (b) highlight, (...)
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  11. Bence Nanay (2011). Function, Modality, Mental Content. Journal of Mind and Behavior 32 (2):84-87.
    I clarify some of the details of the modal theory of function I outlined in Nanay (2010): (a) I explicate what it means that the function of a token biological trait is fixed by modal facts; (b) I address an objection to my trait type individuation argument against etiological function and (c) I examine the consequences of replacing the etiological theory of function with a modal theory for the prospects of using the concept of biological function to explain mental content.
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  12. Bence Nanay (2010). A Modal Theory of Function. Journal of Philosophy 107 (8):412-431.
    The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To able to (...)
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  13. Antonio Nunziante (2008). Back to the Roots. “Functions” and “Teleology” in the Philosophy of Leibniz. In Luca Illetterati & Francesca Michelini (eds.), Purposiveness. Teleology between Nature and Mind. Ontos Verlag.
    It is certainly true that in early modern thought the emergence of a new science changed the image of the universe in a mechanistic way. It must be considered, though, that most of the main protagonists of this revolution (Kepler, Newton, Leibniz, ‘biologists’ like Leeuwenhoek, Hartsoeker, Hooke, Malpighi, Redi, etc.) still continued to consider the importance and the utility of a finalistic explanation of natural phenomena. Concepts like “function”, “self-organization”, “organism” have roots in early modern thought: not only from a (...)
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  14. Jon D. Ringen (1976). Explanation, Teleology, and Operant Behaviorism. Philosophy of Science 43 (June):223-253.
    B. F. Skinner's claim that "operant behavior is essentially the field of purpose" is systematically explored. It is argued that Charles Taylor's illuminating analysis of the explanatory significance of common-sense goal-ascriptions (1) lends some (fairly restricted) support to Skinner's claim, (2) considerably clarifies the conceptual significance of differences between operant and respondent behavior and conditioning, and (3) undercuts influential assertions (e.g., Taylor's) that research programs for behavioristic psychology share a "mechanistic" orientation. A strategy is suggested for assessing the plausibility of (...)
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  15. Scott Sehon, Teleology and Degrees of Freedom.
    There is a debate in philosophy of mind about the nature of reason explanations of action, and this volume is testament to a resurgence of interest in non-causal accounts. In Teleological Realism: Mind, Agency, and Explanation,2 I have proposed a non-causal account according to which common-sense reason explanations of action are irreducibly teleological in form. I claim that we explain behavior by citing the state of affairs towards which the agent was directing her behavior, i. e., by citing the purpose (...)
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  16. Marco Solinas (2015). From Aristotle’s Teleology to Darwin’s Genealogy: The Stamp of Inutility, Basingstoke: Palgrave Macmillan, 2015. Palgrave Macmillan.
    Starting with Aristotle and moving on to Darwin, Marco Solinas outlines the basic steps from the birth, establishment and later rebirth of the traditional view of living beings, and its overturning by evolutionary revolution. The classic framework devised by Aristotle was still dominant in the 17th Century world of Galileo, Harvey and Ray, and remained hegemonic until the time of Lamarck and Cuvier in the 19th Century. Darwin's breakthrough thus takes on the dimensions of an abandonment of the traditional finalistic (...)
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  17. Arno Wouters (2006). What Functions Explain: Functional Explanation and Self-Reproducing Systems. [REVIEW] Acta Biotheoretica 54 (1):55-59.
    Review of Peter Mc. Laughlin *What Functions Explain" (2001).
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Mathematical Explanation
  1. Alan Baker (2009). Mathematical Explanation in Science. British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...)
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  2. Robert W. Batterman (2002). The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. Oxford University Press.
  3. Ingo Brigandt (2013). Explanation in Biology: Reduction, Pluralism, and Explanatory Aims. Science and Education 22 (1):69-91.
    This essay analyzes and develops recent views about explanation in biology. Philosophers of biology have parted with the received deductive-nomological model of scientific explanation primarily by attempting to capture actual biological theorizing and practice. This includes an endorsement of different kinds of explanation (e.g., mathematical and causal-mechanistic), a joint study of discovery and explanation, and an abandonment of models of theory reduction in favor of accounts of explanatory reduction. Of particular current interest are philosophical accounts of complex explanations that appeal (...)
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  4. Ingo Brigandt (2013). Systems Biology and the Integration of Mechanistic Explanation and Mathematical Explanation. Studies in History and Philosophy of Biological and Biomedical Sciences 44 (4):477-492.
    The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have (...)
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  5. O. Bueno & S. French (2012). Can Mathematics Explain Physical Phenomena? British Journal for the Philosophy of Science 63 (1):85-113.
    Batterman ([2010]) raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan ([2011]). Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated (...)
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  6. Christopher Clarke (forthcoming). Multi-Level Selection and the Explanatory Value of Mathematical Decompositions. British Journal for the Philosophy of Science:axv008.
    Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to evaluate their (...)
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  7. Chris Daly & Simon Langford (2009). Mathematical Explanation and Indispensability Arguments. Philosophical Quarterly 59 (237):641-658.
    We defend Joseph Melia's thesis that the role of mathematics in scientific theory is to 'index' quantities, and that even if mathematics is indispensable to scientific explanations of concrete phenomena, it does not explain any of those phenomena. This thesis is defended against objections by Mark Colyvan and Alan Baker.
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  8. Laura Felline (forthcoming). Mechanisms Meet Structural Explanation. Synthese.
    This paper investigates the relationship between Structural Explanation and the New Mechanistic account of explanation. The aim of this paper is twofold: firstly, to argue that some phenomena in the domain of fundamental physics, although mechanically brute, are structurally explained; and secondly, by elaborating on the contrast between SE and ME, to better clarify some features of SE. Finally, this paper will argue that, notwithstanding their apparently antithetical character, SE and ME can be reconciled within a unified account of general (...)
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  9. Laura Felline (2010). Review of R. Batterman: The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction and Emergence. [REVIEW] APhEx – Portale Italiano di Filosofia Analitica.
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  10. Miguel Hoeltje, Benjamin Schnieder & Alex Steinberg (2013). Explanation by Induction? Synthese 190 (3):509-524.
    Philosophers of mathematics commonly distinguish between explanatory and non-explanatory proofs. An important subclass of mathematical proofs are proofs by induction. Are they explanatory? This paper addresses the question, based on general principles about explanation. First, a recent argument for a negative answer is discussed and rebutted. Second, a case is made for a qualified positive take on the issue.
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  11. Marc Lange (2012). Abstraction and Depth in Scientific Explanation. [REVIEW] Philosophy and Phenomenological Research 84 (2):483-491.
  12. M. Liston (2013). Christopher Pincock. Mathematics and Scientific Representation. Oxford University Press, 2012. ISBN 978-0-19-975710-7. Pp. Xv + 330. [REVIEW] Philosophia Mathematica 21 (3):371-385.
  13. Ernan McMullin (2011). Kepler: Moving the Earth. Hopos: The Journal of the International Society for the History of Philosophy of Science 1 (1):3-22.
    The discrepancy between the Aristotelian and the Ptolemaic astronomies led many medievals to regard the latter (and mathematical astronomy generally) as no more than a calculational device. This was the challenge that Copernicus and Kepler had to meet: How was one to show that a mathematically expressed astronomy could indicate that the earth really moves? Copernicus pointed to features of the planetary motions that he could explain but that Ptolemy could not. Kepler went much further. His account of the planetary (...)
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  14. J. B. Paris (1994). The Uncertain Reasoner's Companion: A Mathematical Perspective. Cambridge University Press.
    Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...)
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  15. Christopher Pincock, Mathematical Contributions to Scientific Explanation.
    After reviewing some different indispensability arguments, I distinguish several different ways in which mathematics can make an important contribution to a scientific explanation. Once these contributions are highlighted it will be possible to see that indispensability arguments have little chance of convincing us of the existence of abstract objects, even though they may give us good reason to accept the truth of some mathematical claims. However, in the concluding part of this paper, I argue that even though there is a (...)
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  16. Veikko Rantala (2002). Explanatory Translation. Beyond the Kuhnian Model of Conceptual Change. Kluwer/Springer.
    A systematic attempt to understand cognitive characteristics of translation by bringing its logical, pragmatic, and hermeneutic features together and examining a number of scientific, logical (philosophical and formal),and philosophical applications. The notion of translation investigated here is called explanatory since it is not a translation in the standard, meaning-saving sense but aims to provide an explanation for the meaning change in exact terms.
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  17. T. Raz (2013). On the Application of the Honeycomb Conjecture to the Bee's Honeycomb. Philosophia Mathematica 21 (3):351-360.
    In a recent paper, Aidan Lyon and Mark Colyvan have proposed an explanation of the structure of the bee's honeycomb based on the mathematical Honeycomb Conjecture. This explanation has instantly become one of the standard examples in the philosophical debate on mathematical explanations of physical phenomena. In this critical note, I argue that the explanation is not scientifically adequate. The reason for this is that the explanation fails to do justice to the essentially three-dimensional structure of the bee's honeycomb.
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  18. Alexander Reutlinger (forthcoming). Are Causal Facts Really Explanatorily Emergent? Ladyman and Ross on Higher-Level Causal Facts and Renormalization Group Explanation. Synthese.
    In their Every Thing Must Go, Ladyman and Ross defend a novel version of Neo- Russellian metaphysics of causation, which falls into three claims: (1) there are no fundamental physical causal facts (orthodox Russellian claim), (2) there are higher-level causal facts of the special sciences, and (3) higher-level causal facts are explanatorily emergent. While accepting claims (1) and (2), I attack claim (3). Ladyman and Ross argue that higher-level causal facts are explanatorily emergent, because (a) certain aspects of these higher-level (...)
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  19. Alexander Reutlinger (forthcoming). Why Is There Universal Macro-Behavior? Renormalization Group Explanation As Non-Causal Explanation. Philosophy of Science.
    Renormalization group (RG) methods are an established strategy to explain how it is possible that microscopically different systems exhibit virtually the same macro behavior when undergoing phase-transitions. I argue – in agreement with Robert Batterman – that RG explanations are non-causal explanations. However, Batterman misidentifies the reason why RG explanations are non-causal: it is not the case that an explanation is non- causal if it ignores causal details. I propose an alternative argument, according to which RG explanations are non-causal explanations (...)
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  20. Juha Saatsi (2011). The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science. British Journal for the Philosophy of Science 62 (1):143-154.
    The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.
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  21. Amy M. Schmitter (2000). Mind and Sign: Method and the Interpretation of Mathematics in Descartes's Early Work. Canadian Journal of Philosophy 30 (3):371-411.
  22. David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.
    Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...)
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